Finite Group Databasebeta

← #8464312

Subgroups — #8464312

Order 512.

3875 conjugacy classes of subgroups.

The subgroup lattice has 1489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic
2#59443C211yesmaximal, characteristic
3#59443C211yesmaximal, characteristic
4#58769C214yesmaximal
5#58405C214yesmaximal
6#53767C214yesmaximal
7#53034C212yesmaximal
8#53033C212yesmaximal
9#51302C214yesmaximal
10#46175C212yesmaximal
11#46006C212yesmaximal
12#45414C212yesmaximal
13#45154C212yesmaximal
14#42823C212yesmaximal
15#42820C212yesmaximal
16#42733C212yesmaximal
17#42733C212yesmaximal
18#40107C212yesmaximal
19#39802C212yesmaximal
20#39655C212yesmaximal
21#39625C211yesmaximal, characteristic
22#39181C211yesmaximal, characteristic
23#38976C211yesmaximal, characteristic
24#38976C211yesmaximal, characteristic
25#38970C212yesmaximal
26#37630C211yesmaximal, characteristic
27#37359C212yesmaximal
28#37344C212yesmaximal
29#36563C211yesmaximal, characteristic
30#36563C211yesmaximal, characteristic
31#36447C211yesmaximal, characteristic
32#35199C211yesmaximal, characteristic
33#35187C211yesmaximal, characteristic
34#34951C211yesmaximal, characteristic
35#34920C211yesmaximal, characteristic
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2862C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2212yes—
44#2859C2212yes—
45#2844C2214yes—
46#2843C2214yes—
47#2843C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2833C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2805C2214yes—
54#2805C2214yes—
55#2802C2214yes—
56#2794C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2789C2214yes—
62#2789C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2769C2214yes—
73#2769C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2762C2214yes—
82#2762C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2755C2214yes—
87#2734C2214yes—
88#2734C2214yes—
89#2726C2214yes—
90#2719C2214yes—
91#2719C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2713C2214yes—
101#2713C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2666C2214yes—
105#2666C2214yes—
106#2660C2214yes—
107#2660C2212yes—
108#2655C2214yes—
109#2655C2214yes—
110#2647C2212yes—
111#2647C2212yes—
112#2645C2212yes—
113#2645C2212yes—
114#2645C2212yes—
115#2645C2212yes—
116#2642C2214yes—
117#2642C2212yes—
118#2606C2214yes—
119#2605C2214yes—
120#2590C2212yes—
121#2588C2212yes—
122#2588C2214yes—
123#2585C2212yes—
124#2585C2214yes—
125#2585C2212yes—
126#2584C2211yescharacteristic
127#2582C2211yescharacteristic
128#2582C2211yescharacteristic
129#2582C2211yescharacteristic
130#2582C2211yescharacteristic
131#2582C2212yes—
132#2581C2212yes—
133#2581C2212yes—
134#2581C2212yes—
135#2581C2211yescharacteristic
136#2571C2211yescharacteristic
137#2571C2212yes—
138#2571C2212yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2568C2211yescharacteristic
143#2568C2211yescharacteristic
144#2568C2211yescharacteristic
145#2568C2211yescharacteristic
146#2567C2212yes—
147#2567C2212yes—
148#2567C2212yes—
149#2567C2212yes—
150#2565C2212yes—
151#2565C2212yes—
152#2565C2211yescharacteristic
153#2552C2212yes—
154#2552C2212yes—
155#2552C2211yescharacteristic
156#2552C2211yescharacteristic
157#2552C2212yes—
158#2551C2212yes—
159#2551C2211yescharacteristic
160#2551C2212yes—
161#2551C2212yes—
162#2550C2212yes—
163#2550C2214yes—
164#2550C2212yes—
165#2550C2212yes—
166#2550C2211yescharacteristic
167#2546C2212yes—
168#2546C2211yescharacteristic
169#2546C2211yescharacteristic
170#2533C2214yes—
171#2533C2214yes—
172#2528C2214yes—
173#2528C2214yes—
174#2528C2214yes—
175#2528C2214yes—
176#2524C2214yes—
177#2524C2214yes—
178#2524C2214yes—
179#2524C2214yes—
180#2520C2214yes—
181#2520C2212yes—
182#2514C2214yes—
183#2514C2212yes—
184#2514C2212yes—
185#2514C2212yes—
186#2514C2212yes—
187#2514C2212yes—
188#2514C2212yes—
189#2514C2212yes—
190#2514C2212yes—
191#2511C2212yes—
192#2511C2212yes—
193#2511C2212yes—
194#2511C2212yes—
195#2511C2212yes—
196#2511C2212yes—
197#2511C2211yescharacteristic
198#2511C2211yescharacteristic
199#2511C2212yes—
200#2509C2214yes—
201#2509C2212yes—
202#2509C2212yes—
203#2509C2212yes—
204#2508C2214yes—
205#2508C2212yes—
206#2508C2212yes—
207#2508C2212yes—
208#2508C2212yes—
209#2508C2212yes—
210#2508C2211yescharacteristic
211#2507C2212yes—
212#2507C2212yes—
213#2507C2212yes—
214#2507C2214yes—
215#2506C2214yes—
216#2506C2212yes—
217#2506C2212yes—
218#2506C2212yes—
219#2506C2212yes—
220#2506C2212yes—
221#2506C2211yescharacteristic
222#2462C2212yes—
223#2453C2211yescharacteristic
224#2453C2212yes—
225#2453C2212yes—
226#2451C2212yes—
227#2451C2212yes—
228#2451C2212yes—
229#2451C2212yes—
230#2451C2212yes—
231#2451C2212yes—
232#2451C2212yes—
233#2451C2211yescharacteristic
234#2451C2212yes—
235#2446C2212yes—
236#2446C2212yes—
237#2446C2212yes—
238#2446C2212yes—
239#2446C2212yes—
240#2446C2211yescharacteristic
241#2446C2212yes—
242#2446C2212yes—
243#2446C2211yescharacteristic
244#2402C2212yes—
245#2402C2212yes—
246#2402C2212yes—
247#2399C2212yes—
248#2382C2214yes—
249#2369C2212yes—
250#2369C2212yes—
251#2365C2212yes—
252#2356C2212yes—
253#2356C2212yes—
254#2356C2212yes—
255#2356C2212yes—
256#2355C2211yescharacteristic
257#2355C2211yescharacteristic
258#2355C2212yes—
259#2355C2212yes—
260#2355C2212yes—
261#2351C2212yes—
262Q8×C4⋊C4C2211yescharacteristic
263Q8×C4⋊C4C2211yescharacteristic
264Q8×C4⋊C4C2211yescharacteristic
265Q8×C4⋊C4C2212yes—
266Q8×C4⋊C4C2212yes—
267Q8×C4⋊C4C2211yescharacteristic
268#2336C2214yes—
269#2331C2212yes—
270#2331C2212yes—
271#2330C2212yes—
272#2327C2212yes—
273#2320C2212yes—
274#2320C2212yes—
275#2320C2212yes—
276#2320C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2212yes—
283C4×C4⋊Q8C2211yescharacteristic
284C4×C4⋊Q8C2211yescharacteristic
285C4×#125C2211yescharacteristic
286C4×#125C2211yescharacteristic
287C4×#125C2212yes—
288C4×#125C2212yes—
289C4×#125C2212yes—
290#2295C2211yescharacteristic
291#2295C2212yes—
292#2295C2211yescharacteristic
293#2295C2211yescharacteristic
294#2295C2211yescharacteristic
295#2295C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×Q8C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2311yescharacteristic
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2314yes—
311C2×C4⋊Q8C2314yes—
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2311yescharacteristic
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#125C2312yes—
319C2×#125C2314yes—
320C2×#125C2312yes—
321C2×#125C2314yes—
322C2×#125C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2311yescharacteristic
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342#401C2314yes—
343#401C2314yes—
344#401C2314yes—
345#401C2314yes—
346#401C2314yes—
347#401C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2312yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2312yes—
395#400C2312yes—
396#400C2312yes—
397#400C2312yes—
398#400C2312yes—
399#400C2314yes—
400#400C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2312yes—
407#398C2314yes—
408#398C2312yes—
409#398C2312yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2312yes—
418#398C2312yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2312yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2312yes—
431#398C2312yes—
432#398C2314yes—
433#398C2312yes—
434#398C2312yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2312yes—
439#398C2312yes—
440#398C2312yes—
441#398C2312yes—
442#398C2314yes—
443#398C2312yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2312yes—
461#395C2312yes—
462#395C2312yes—
463#395C2312yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#391C2311yescharacteristic
469#391C2311yescharacteristic
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#391C2311yescharacteristic
487#391C2312yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2311yescharacteristic
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2311yescharacteristic
518#391C2312yes—
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2311yescharacteristic
575#389C2311yescharacteristic
576#389C2312yes—
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2314yes—
580#389C2314yes—
581#389C2312yes—
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2312yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2314yes—
591#389C2314yes—
592#389C2314yes—
593#389C2314yes—
594#389C2314yes—
595#389C2312yes—
596#389C2311yescharacteristic
597#389C2314yes—
598#389C2311yescharacteristic
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2312yes—
602#389C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#387C2312yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2314yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2312yes—
692#387C2312yes—
693#384C2311yescharacteristic
694#384C2312yes—
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2311yescharacteristic
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2314yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2314yes—
709#384C2312yes—
710#383C2314yes—
711#383C2314yes—
712#383C2314yes—
713#383C2314yes—
714#383C2314yes—
715#383C2314yes—
716#383C2314yes—
717#383C2314yes—
718#383C2314yes—
719#382C2311yescharacteristic
720#382C2312yes—
721#382C2312yes—
722#382C2311yescharacteristic
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2312yes—
729#382C2312yes—
730#382C2314yes—
731#382C2314yes—
732#382C2314yes—
733#382C2314yes—
734#382C2314yes—
735#382C2314yes—
736#382C2314yes—
737#382C2314yes—
738#382C2312yes—
739#382C2312yes—
740#382C2314yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2314yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799#376C2312yes—
800#376C2312yes—
801#376C2312yes—
802#376C2312yes—
803#376C2314yes—
804#376C2314yes—
805C43C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2312yes—
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2412yes—
814C22×Q8C2411yescharacteristic
815C22×Q8C2411yescharacteristic
816C22×Q8C2412yes—
817C22×Q8C2414yes—
818C22×Q8C2414yes—
819C4⋊Q8—24no—
820C4⋊Q8—24no—
821C4⋊Q8—24no—
822C4⋊Q8—42no—
823C4⋊Q8—44no—
824C4⋊Q8—44no—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—42no—
828C4⋊Q8—44no—
829C4⋊Q8—84no—
830C4⋊Q8—84no—
831C4⋊Q8—82no—
832#125—28no—
833#125—28no—
834#125—24no—
835#125—42no—
836#125—44no—
837#125—82no—
838#125—84no—
839#125—84no—
840#125—82no—
841#125—84no—
842#125—84no—
843C4×Q8—24no—
844C4×Q8—28no—
845C4×Q8—24no—
846C4×Q8—28no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—24no—
852C4×Q8—24no—
853C4×Q8—44no—
854C4×Q8—42no—
855C4×Q8—44no—
856C4×Q8—44no—
857C4×Q8—44no—
858C4×Q8—44no—
859C4×Q8—44no—
860C4×Q8—42no—
861C4×Q8—42no—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2411yescharacteristic
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2414yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2411yescharacteristic
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2414yes—
1004C2×C42C2414yes—
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2411yescharacteristic
1034#95C2412yes—
1035#95C2411yescharacteristic
1036#95C2411yescharacteristic
1037#95C2412yes—
1038#95C2411yescharacteristic
1039#95C2412yes—
1040#95C2411yescharacteristic
1041#95C2412yes—
1042#95C2412yes—
1043#95C2411yescharacteristic
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2414yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116C2×Q8—22no—
1117C2×Q8—22no—
1118C2×Q8—22no—
1119C2×Q8—22no—
1120C2×Q8—22no—
1121C2×Q8—24no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—22no—
1126C2×Q8—22no—
1127C2×Q8—22no—
1128C2×Q8—24no—
1129C2×Q8—22no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—41no—
1133C2×Q8—42no—
1134C2×Q8—42no—
1135C2×Q8—42no—
1136C2×Q8—44no—
1137C2×Q8—44no—
1138C2×Q8—44no—
1139C2×Q8—44no—
1140C2×Q8—44no—
1141C2×Q8—44no—
1142C2×Q82−1+414yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2514yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2514yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C4⋊C4—22no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—22no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—22no—
1188C4⋊C4—24no—
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—22no—
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—41no—
1228C4⋊C4—41no—
1229C4⋊C4—42no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—41no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—42no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—42no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—42no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C42−1+414yes—
1280C42—22no—
1281C42—22no—
1282C42—22no—
1283C42—24no—
1284C42—22no—
1285C42—24no—
1286C42—28no—
1287C42—22no—
1288C42—24no—
1289C42—28no—
1290C42—24no—
1291C42—24no—
1292C42—24no—
1293C42—22no—
1294C42—24no—
1295C42—24no—
1296C42—24no—
1297C42—22no—
1298C42—22no—
1299C42—24no—
1300C42—22no—
1301C42—22no—
1302C42—22no—
1303C42—22no—
1304C42—24no—
1305C42—22no—
1306C42—22no—
1307C42—24no—
1308C42—44no—
1309C42—42no—
1310C42—42no—
1311C42—44no—
1312C42—44no—
1313C42—44no—
1314C42—44no—
1315C42—41no—
1316C42—42no—
1317C42—41no—
1318C42—42no—
1319C42—44no—
1320C42—44no—
1321C42—41no—
1322C422−1+414yes—
1323C422−1+414yes—
1324C23C2611yescharacteristic
1325Q8—28no—
1326Q8—44no—
1327Q8—44no—
1328Q8—48no—
1329Q8—44no—
1330Q8—44no—
1331Q8—84no—
1332Q8—164no—
1333Q8—164no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—24no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—22no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—21no—
1422C2×C4—22no—
1423C2×C4—24no—
1424C2×C4—21no—
1425C2×C4—24no—
1426C2×C4C2×2−1+412yes—
1427C2×C4C2×2−1+412yes—
1428C2×C4C2×2−1+414yes—
1429C2×C4C2×2−1+412yes—
1430C2×C4C2×2−1+412yes—
1431C2×C4C2×2−1+412yes—
1432C2×C4C2×2−1+412yes—
1433C2×C4C2×2−1+412yes—
1434C2×C4C2×2−1+412yes—
1435C2×C4C2×2−1+412yes—
1436C2×C4C2×2−1+412yes—
1437C2×C4#58512yes—
1438C2×C4#58512yes—
1439C22C22×2−1+411yescharacteristic
1440C22C22×2−1+411yescharacteristic
1441C22C22×2−1+411yescharacteristic
1442C22C22×2−1+411yescharacteristic
1443C22C2×#58511yescharacteristic
1444C22C2×#58511yescharacteristic
1445C22H(7,𝔽2)11yescharacteristic
1446C4—24no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4—44no—
1457C4—42no—
1458C4—41no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—41no—
1463C4—41no—
1464C4—42no—
1465C4—42no—
1466C4—44no—
1467C4—41no—
1468C4—42no—
1469C4—42no—
1470C4—42no—
1471C4—41no—
1472C4—42no—
1473C4—41no—
1474C4—42no—
1475C4—44no—
1476C4—42no—
1477C4—44no—
1478C4—41no—
1479C4#355514yes—
1480C4#356314yes—
1481C2C2×#356311yescharacteristic
1482C2C2×#355511yescharacteristic
1483C2#6283711yescharacteristic
1484C2#6294311yescharacteristic
1485C2#6294311yescharacteristic
1486C2#6296611yescharacteristic
1487C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598702
#594432
#587692
#584052
#537672
#530342
#530332
#513022
#461752
#460062
#454142
#451542
#428232
#428202
#427332
#401072
#398022
#396552
#396252
#391812
#389762
#389702
#376302
#373592
#373442
#365632
#364472
#351992
#351872
#349512
#349202